Theoretical models of time-space: the role of transport networks in the shrinking and shrivelling of geographical space Alain L’Hostis, Université Paris-Est, LVMT, Inrets Keywords Contraction, time-space convergence, time-space, cartography, shrinking, shrivelling, theoretical models Abstract Understanding distances between places is a fundamental task for the geographer, while the representation of distances constitutes one of the major functions of cartography. This is why time-distance representation constitutes a key tool for the contemporary geographer. The purpose of this chapter is, in a first step, to expose a set of solutions to the cartographical representations of distances as transformed by transport means. In a second step we will discuss the relations between these cartographical solutions and the theoretical geographical discourse on time-space structured around classical theoretical models. Introduction Understanding distances between places is a fundamental task for the geographer, while the representation of distances constitutes one of the major functions of cartography. This is why time-distance representation constitutes a key tool for the contemporary geographer. Among the types of maps introduced to represent time-space anamorphoses were supplemented with time-space relief cartography in the 1990s. On the one hand the present globalisation process has only been made possible through a reduction in time-distances allowed by high speeds, and particularly through the development of air transport. On the other hand the metropolitanization process seen as the urban counterpart of globalisation is deeply associated with the development of air platforms. Both phenomena are intrinsically linked to the formation of distances, and especially time- distances. The purpose of this chapter is, in a first step, to expose a set of solutions to the cartographical representations of distances as transformed by transport means. In a second step we will discuss the relations between these cartographical solutions and the theoretical geographical discourse on time-space structured around classical theoretical models. 1. Transport networks produce distances: a cartographic problem To understand the present global space it is necessary to underline the major role played by high speeds in the structuring of metropolitan spaces. These high speeds have allowed the development of communications on a global scale. But, in the mean time, high speeds operate a dramatic selection of places. While this movement highlights the high places of global communication, the secondary networks and spaces remain present in the interstices. A key point in the formation of global time-distances is the fact that these secondary networks are disqualified when compared to the main high-speed networks. In view of these phenomena the recent literature insists on the differentiation of space where global functions can be located in the close spatial neighbourhood of spaces of dereliction and exclusion (Graham and Marvin 2001) and on inequalities in space favouring largest centres (Knowles 2006). Figure 1 : the phenomenon of spatial inversion But how to represent this complicated set of networks and relations in space? To tackle this question means considering the broader perspective of the representation of distances. In this field Bunge has stated that basically two ways are available either “representing complicated distances on simple maps, or representing simple distances on complicated maps” (Bunge 1962). In his classical example of the complicated relations in space generated by contemporary transport means, Bunge considers the movements from intermediary space to higher level cities with a trip from somewhere in Montana to the metropolis of Chicago. The articulation of transport modes, here cars and planes, implies in this example that the shortest path in time space takes a completely different shape beyond and after a particular point of indifference. Leaving from Butte would mean driving directly to Chicago, while starting from somewhere closer to the Pacific coast involves a trip by car to Seattle followed by a flight. This phenomenon of spatial inversion that follows an intuitive logic from a transport perspective provokes a disturbance in the order of proximities. If we refer to Cauvins’s formalism (Cauvin 1984), while the Rocky Mountains are located between Seattle and Chicago in chorotaxic space –the usual geographic space- their position in functional space is different: in the transport space it is Seattle that stands between the Rocky mountains and the Great Lakes. The identification of the phenomenon of spatial inversion constitutes a key justification of the research of new representations of time-space that would render this complicated set of distances. It is a direct call to complicate the map in order to allow the representation of distances that would be simpler to read. In this perspective, time-space anamorphic cartography is the first proposal in which one moves the locations in order to better respect time-distances. An example is given by Shimizu showing the contraction of Japan due to the development of the high-speed train networks between 1962 and 1992 (Shimizu 1992). In the field of the representation of distances, anamorphosis belongs to the type of cartography defined by Bunge as simpler distances on a complicated map. Two elements of information on time-distances can be read from such a representation: the overall space contraction and the local deformations produced by high- speed lines. If the new transport networks had been characterised by homogeneity and anisotropy the shape of the external borders of the country would have remained unchanged.. Only size would have been reduced. All the distortions from the usual and conventional shape of Japan indicate directions privileged by the shape of the networks. The literature on networks has abundantly expressed the idea that modern transport provokes heterogeneousness in space (Dupuy 1991; Castells 1996; Graham and Marvin 2001; Knowles 2006). This model, however, is subject to limitations . The major criticism of the application of anamorphosis to the representation of distances is the fact that if two locations, for instance two cities, are getting closer due to a new transport link, this does not mean that the space in between is also gaining in accessibility. Toll motorways are examples of the “tunnel effect” of some infrastructures where the limited access points reduce the accessibility gains to a set of subspaces, and is not distributed evenly along the line (Plassard 1976). This phenomenon is even more pronounced in the case of high-speed rail (Murayama 1994; Mathis 2007) and is one of the major characteristics of air transport (Haggett 2001). Furnishing an illustration of this limitation, the phenomenon of spatial inversion cannot be read from the anamorphic map because of the principle of the preservation of the order of proximities which can be found in most methods developed in the literature (Shimizu 1992; Spiekermann and Wegener 1994; Clark 1999; Kotoh 2001). Displacing the locations on the map is not the only way in which distances can be represented. The idea of drawing the transport lines between places in such a way that different distances are shown was introduced in the 1980’s (Plassard and Routhier 1987; Tobler 1997). In the example proposed by Tobler, location of cities and network nodes remains unchanged, as compared to their usual cartographic position. The length of roads between the nodes is displayed in the form of a spring, the intensity of the tension indicating the sinuousness of roads unevenly distributed in this mountainous area in western Colorado. In this model one can obtain the information on the difficulty of linking two places by reading the visual length of the links. The notion of visual length was introduced (L'Hostis 2003) to render account of the capacity of a reader of a map to extract the information on the length of a route from the analysis of the shape of the path. A straight segment can be converted in kilometres through a direct use of the scale, while a sinuous curve will indicate a longer road. This principle is used in the spring map to express the idea of privileged and handicapped directions. Figure 2 : spring map of roads in western Colorado The spring map model can indicate the shortest directions in space. Being a non-Euclidean representation, it displays the idea that the shortest paths often differ from the straight line. In this perspective, it constitutes a possible proposal to the call for non-Euclidean geography (Golledge and Hubert 1982; Müller 1982). More recently, but in the same direction, a model has been formulated to introduce a three dimensional surface that allows the representation of different speeds in urban space (Hyman and Mayhew 2004). Sharing a principle of construction similar to that of the spring map, the time-space relief map was introduced in the 1990s (Mathis, Polombo et al. 1993; L'Hostis 1996; Mathis 1996). This type of representation preserves the location of places but exploits the resources of the third dimension to draw the various speeds and the corresponding time-distances in a multimodal network. 2. Air and road modes as major inter- and intra-metropolitan transport systems Globalisation, considered together with metropolitanization as its urban counterpart, is being made possible by the development of efficient, long-haul and short-haul transport systems. If metropolises can be defined as urban entities that communicate on a global scale, the air mode constitutes the major passenger transport system associated with globalisation (Sassen 1991; Haggett 2001). Indeed, the equipment of metropolises with airport infrastructure, the number of flights and destinations available or the air distances are often used as indicators of the position of cities in the global competition (Grubesic and Zook 2007) . Nevertheless, the development of the air mode during the 20 th century and beyond has not lead to the replacement of other slower transport systems. Each transport mode has developed inside its own space of predominance, with fierce competition in the margins.